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Lloyd Shapley was born on June 2, 1923, in Cambridge, Massachusetts, one of the sons of Martha (Betz) and the distinguished astronomer Harlow Shapley, both from Missouri.^{[5]} He attended Phillips Exeter Academy and was a student at Harvard when he was drafted in 1943. He served in the Army Air Corps in Chengdu, China and received the Bronze Star decoration for breaking the Soviet weather code.^{[6]} After the war, he returned to Harvard and graduated with an A.B. in mathematics in 1948. After working for one year at the RAND Corporation, he went to Princeton University where he received a Ph.D. in 1953. His thesis and post-doctoral work introduced the Shapley value and the core solution in game theory. After graduating, he remained at Princeton for a short time before going back to the RAND corporation from 1954 to 1981. Since 1981 he has been a professor at UCLA.

Along with the Shapley value, stochastic games, the Bondareva–Shapley theorem (which implies that convex games have non-empty cores), the Shapley–Shubik power index (for weighted or block voting power), the Gale–Shapley algorithm (for the stable marriage problem), the concept of a potential game (with Dov Monderer), the Aumann–Shapley pricing, the Harsanyi–Shapley solution, the Snow–Shapley theorem for matrix games, and the Shapley–Folkman lemma & theorem bear his name.

Besides, his early work with R.N.Snow and Samuel Karlin on matrix games was so complete that little has been added since. He has been instrumental in the development of utility theory, and it was he who laid much of the groundwork for the solution of the problem of the existence of Von Neumann–Morgenstern stable sets. His work with M.Maschler and B.Peleg on the kernel and the nucleolus, and his work with Robert Aumann on non-atomic games and on long-term competition have all had a tremendous impact in economic theory.

In his 80s, Shapley continues publishing in the areas of specialization he created or advanced, such as multi-person utility (with Manel Baucells) and authority distribution (a generalization to the Shapley–Shubik power index and useful in ranking, planning and group decision-making).

## Finding Stable Matches

How to bring different players together in the best possible way is a key economic problem. Examples of situations where this problem arises include matching children with different schools, and kidneys or other organs with patients who require transplants. From the 1960s onward, Lloyd Shapley used what is known as Cooperative Game Theory to study different matching methods. Within the framework of this theory, it is especially important that a stable match is found. A stable match entails that there are no two agents who would prefer one another over their current counterparts. In collaboration with other researchers, Shapley has succeeded in identifying methods that achieve this stability.

Beginning in the 1980s, Alvin Roth used Shapley's theoretical results to explain how markets function in practice. Through empirical studies and lab experiments, Roth and his colleagues demonstrated that stability was critical to successful matching methods. Roth has also developed systems for matching doctors with hospitals, school pupils with schools, and organ donors with patients.

**Employment**:

- U.S. Army, 1943-1945

- Rand Corporation, research mathematician, 1948-49, 1954-81

- Princeton University, Fine Instructor, 1952-54

- University of California, Los Angeles, 1981-

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